FRM Part I · FRM Exam Part I · Properties of Interest Rates
A bank quotes a deposit rate of 6% per annum with semiannual compounding. What is the equivalent annual rate with annual compounding, to the nearest 0.01%?
The equivalent annual rate is 6.09%. Semiannual compounding at 6% means 3% is earned every six months, so growth over one year is 1.03 squared, or 1.0609. Subtracting one gives 6.09%, which is higher than the nominal 6% because interest earns interest.
- A6.00%
- B6.09%Correct
- C6.18%
- D6.14%
Explanation
Equivalent annual rate = (1 + 0.06/2)^2 - 1 = 1.03^2 - 1 = 1.0609 - 1 = 6.09%. Option 6.00% ignores compounding. 6.18% would be the rate with monthly-style over-compounding error, and 6.14% is the continuously compounded equivalent, e^0.06 - 1, which does not apply here.
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